merge: T89 branches table + projector handlers

chat/db/migrations/0013_branches.sql

@@ -0,0 +1,17 @@
+CREATE TABLE branches (
+    id INTEGER PRIMARY KEY,
+    name TEXT NOT NULL UNIQUE,
+    origin_event_id INTEGER NOT NULL,
+    head_event_id INTEGER NOT NULL,
+    chat_id TEXT,
+    created_at TEXT NOT NULL DEFAULT (datetime('now')),
+    is_active INTEGER NOT NULL DEFAULT 0
+);
+
+-- Exactly one row may have is_active = 1 at any time.
+CREATE UNIQUE INDEX branches_active_idx ON branches(is_active) WHERE is_active = 1;
+
+-- Bootstrap the main branch. origin_event_id=0 + head_event_id=0 are
+-- placeholder seeds; the orchestrator updates head as new events land.
+INSERT INTO branches (name, origin_event_id, head_event_id, is_active)
+VALUES ('main', 0, 0, 1);